Question

The first three terms of an arithmetic progression are 5x, 2x+3, and 2x+7 respectively. Find the value of x

Answer 1

$a_1=5x$

$a_1+d=2x+3$

$a_1+2d=2x+7$

Substituting for the value $a_1$

$5x+d=2x+3$

$5x+2d=2x+7$

Forming simultaneous equation and solving by substitution ;

$3x+d=3$

$3x+2d=7$

$d=3-3x$

$6-6x+3x=7$

$6-3x=7$

$3x=13$

$x=\frac{13}{3}$